Elementary Theory of L-functions and Eisenstein Series [Hardcover]

An elementary but detailed insight into the theory of L-functions. The presentation is self contained and concise.The approach is basically algebraic and the treatment elementary in this comprehensive and systematic account of the theory of p-adic and classical modular forms and the theory of the special values of arithmetic L-functions and p-adic L-functions.The approach is basically algebraic and the treatment elementary in this comprehensive and systematic account of the theory of p-adic and classical modular forms and the theory of the special values of arithmetic L-functions and p-adic L-functions.This book is a comprehensive and systematic account of the theory of p-adic and classical modular forms and the theory of the special values of arithmetic L-functions and p-adic L-functions. The approach is basically algebraic, and the treatment is elementary. No deep knowledge from algebraic geometry and representation theory is required. The author's main tool in dealing with these problems is taken from cohomology theory over Riemann surfaces, which is also explained in detail in the book. He also gives a concise but thorough treatment of analytic continuation and functional equation. Graduate students wishing to know more about L-functions will find this a unique introduction to this fascinating branch of mathematics.Suggestions to the reader; 1. Algebraic number theory; 2. Classical L-functions and Eisenstein series; 3. p-adic Hecke L-functions; 4. Homological interpretation; 5. Elliptical modular forms and their L-functions; 6. Modular forms and cohomology groups; 7. Ordinary L-adic forms, two-variable p-adic Rankin products and Galois representations; 8. Functional equations of Hecke L-functions; 9. Adelic Eisenstein series and Rankin products; 10. Three-variable p-adic Rankin products; Appendix; References; Answers to selected exercises; Index. ...its style is unusually lively; even in the exposition of classical results, one feels that the proof has been rel³1